Solve for $x$ and $y$ using elimination. ${4x-3y = 29}$ ${-3x+2y = -22}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $4$ ${12x-9y = 87}$ $-12x+8y = -88$ Add the top and bottom equations together. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {4x-3y = 29}\thinspace$ to find $x$ ${4x - 3}{(1)}{= 29}$ $4x-3 = 29$ $4x-3{+3} = 29{+3}$ $4x = 32$ $\dfrac{4x}{{4}} = \dfrac{32}{{4}}$ ${x = 8}$ You can also plug ${y = 1}$ into $\thinspace {-3x+2y = -22}\thinspace$ and get the same answer for $x$ : ${-3x + 2}{(1)}{= -22}$ ${x = 8}$